Finite edge-primitive graphs of prime valency

被引：9

作者：

Pan, Jiangmin ^{[1
]}

Wu, Cixuan ^{[1
]}

Yin, Fugang ^{[1
]}

机构：

[1] Yunnan Univ Finance & Econ, Sch Stat & Math, Kunming, Yunnan, Peoples R China

来源：

EUROPEAN JOURNAL OF COMBINATORICS | 2018年 / 73卷

基金：

中国国家自然科学基金;

关键词：

ARC-TRANSITIVE GRAPHS; PERMUTATION-GROUPS; CAYLEY-GRAPHS; STABILIZERS;

D O I：

10.1016/j.ejc.2018.05.006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Many famous graphs are edge-primitive. Weiss (1973) and Guo et al. (2013) determined edge-primitive graphs of valency 3 and 5, respectively. In this paper, we study edge-primitive graphs of any prime valency. It is proved that all such graphs are 2-arc-transitive and the full automorphism groups are almost simple with the only exception the graphs being the complete bipartite graphs, and a complete classification is given of such graphs with soluble edge stabilizers, which widely extends the classifications of Weiss and Guo et al. (notice that the edge stabilizers of edge-primitive graphs with valency at most 5 are soluble). (C) 2018 Elsevier Ltd. All rights reserved.

引用

页码：61 / 71

页数：11

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